Ollivier-Ricci idleness functions of graphs
- We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.
| Author details: | D. P. Bourne, D. Cushing, S. Liu, Florentin MünchGND, Norbert PeyerimhoffGND |
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| DOI: | https://doi.org/10.1137/17M1134469 |
| ISSN: | 0895-4801 |
| ISSN: | 1095-7146 |
| Title of parent work (English): | SIAM Journal on Discrete Mathematics |
| Publisher: | Society for Industrial and Applied Mathematics |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/06/19 |
| Publication year: | 2018 |
| Release date: | 2022/03/25 |
| Tag: | Ollivier-Ricci; idleness; optimal transport |
| Volume: | 32 |
| Issue: | 2 |
| Number of pages: | 17 |
| First page: | 1408 |
| Last Page: | 1424 |
| Funding institution: | German National Merit Foundation |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
